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Trigonometry Section 1.1

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

An escalator in a department store is to carry people a vertical distance of 22 feet between floors. How long is the escalator if it makes an angle of 30mc001-1.jpg with the ground?
a.
42 feet
b.
39 feet
c.
46 feet
d.
44 feet
e.
37 feet
 

 2. 

The object shown in the figure is a cube (all edges are equal in length).

mc002-1.jpg

If the length of each edge of the cube shown in the figure is 5 inches, find the length of diagonal CB.
a.
mc002-2.jpg inches
b.
mc002-3.jpg inches
c.
mc002-4.jpg inches
d.
mc002-5.jpg inches
e.
mc002-6.jpg inches
 

 3. 

The object shown in the figure is a cube (all edges are equal in length).

mc003-1.jpg

Suppose the length of diagonal mc003-2.jpg in the figure is mc003-3.jpg feet. What is the length of edge mc003-4.jpg?
a.
mc003-5.jpg inches
b.
mc003-6.jpg inches
c.
mc003-7.jpg inches
d.
mc003-8.jpg inches
e.
mc003-9.jpg inches
 

 4. 

Find the remaining sides of a mc004-1.jpg triangle if the longest side is mc004-2.jpg.
a.
mc004-3.jpg
b.
mc004-4.jpg
c.
mc004-5.jpg
d.
mc004-6.jpg
e.
mc004-7.jpg
 

 5. 

Find the remaining sides of a mc005-1.jpg triangle if the side opposite mc005-2.jpg is mc005-3.jpg.
a.
mc005-4.jpg
b.
mc005-5.jpg
c.
mc005-6.jpg
d.
mc005-7.jpg
e.
mc005-8.jpg
 

 6. 

Find mc006-1.jpg if  mc006-2.jpg, mc006-3.jpg, and mc006-4.jpg.

mc006-5.jpg
a.
mc006-6.jpg
b.
mc006-7.jpg
c.
mc006-8.jpg
d.
mc006-9.jpg
e.
mc006-10.jpg
 

 7. 

Find mc007-1.jpg if mc007-2.jpg and mc007-3.jpg.

mc007-4.jpg
a.
mc007-5.jpg
b.
mc007-6.jpg
c.
mc007-7.jpg
d.
mc007-8.jpg
e.
mc007-9.jpg
 

 8. 

A searchlight rotates through one complete revolution every 2 seconds. How long does it take the light to rotate through 180mc008-1.jpg?
a.
4 sec.
b.
5 sec.
c.
7 sec.
d.
2 sec.
e.
1 sec.
 

 9. 

Find mc009-1.jpg if  mc009-2.jpgmc009-3.jpg and  mc009-4.jpg.

mc009-5.jpg

Remember: The sum of the three angles in any triangle is always 180mc009-6.jpg.
a.
mc009-7.jpg
b.
mc009-8.jpg
c.
mc009-9.jpg
d.
mc009-10.jpg
e.
mc009-11.jpg
 

 10. 

Indicate if the angle mc010-1.jpg is acute or obtuse. Then give the complement and the supplement of the angle.
a.
acute;
complement: mc010-2.jpgsupplement: mc010-3.jpg
b.
obtuse;
complement: mc010-4.jpgsupplement: mc010-5.jpg
c.
obtuse;
complement: mc010-6.jpgsupplement: mc010-7.jpg
d.
acute;
complement: mc010-8.jpgsupplement: mc010-9.jpg
e.
obtuse;
complement: mc010-10.jpgsupplement: mc010-11.jpg
 

Numeric Response
 

 11. 

An escalator in a department store is to carry people a vertical distance of  15 feet between floors. How long is the escalator if it makes an angle of 30nr011-1.jpg with the ground?

__________ feet.

 

 12. 

The object shown in the figure is a cube (all edges are equal in length).

nr012-1.jpg

Suppose the length of the diagonal nr012-2.jpg in the figure is nr012-3.jpg feet. What is the length of edge nr012-4.jpg?

 

 13. 

Suppose nr013-1.jpg is a right triangle with nr013-2.jpg.

If  nr013-3.jpg and  nr013-4.jpg, find nr013-5.jpg.

 

 14. 

Suppose nr014-1.jpg is a right triangle with nr014-2.jpg.

If  nr014-3.jpg and  nr014-4.jpg, find nr014-5.jpg.

 

 15. 

Find nr015-1.jpg if nr015-2.jpg and nr015-3.jpg.

nr015-4.jpg

 

 16. 

Solve for nr016-1.jpg

nr016-2.jpg

 

 17. 

Find nr017-1.jpg  if A = nr017-2.jpg.

nr017-3.jpg

Remember: The sum of the three angles in any triangle is always 180°

nr017-4.jpg __________°

 

 18. 

The figure shows a walkway with a handrail. Angle nr018-1.jpg is the angle between the walkway and the horizontal, while anglenr018-2.jpg is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal.

nr018-3.jpg

Find nr018-4.jpg if  nr018-5.jpg.

nr018-6.jpg__________°

 

 19. 

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 60nr019-1.jpg, what is the measure of the base angles?

__________nr019-2.jpg

 

 20. 

Find nr020-1.jpg if nr020-2.jpgnr020-3.jpg and  nr020-4.jpg.

nr020-5.jpg

Remember: The sum of the three angles in any triangle is always 180nr020-6.jpg.

nr020-7.jpg __________ nr020-8.jpg

 

Short Answer
 

 21. 

Indicate if the angle sa021-1.jpg is acute or obtuse. __________

Give the complement angle. __________sa021-2.jpg

Give the supplement angle. __________sa021-3.jpg
 

 22. 

Find sa022-1.jpg if  sa022-2.jpg, sa022-3.jpg, and sa022-4.jpg.
sa022-5.jpg

Simplify the answer. Do not convert to decimal form.
 

 23. 

Give the complement angle of angle sa023-1.jpg. __________

Give the supplement angle of angle sa023-2.jpg. __________
 

 24. 

Find the remaining sides of a sa024-1.jpg triangle if the side opposite sa024-2.jpg is sa024-3.jpg.
 

 25. 

Find the remaining side of a sa025-1.jpg triangle if the shorter sides are each sa025-2.jpg.
 



 
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